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Persistent homology (PH) -- the conventional method in topological data analysis -- is computationally expensive, requires further vectorization of its signatures before machine learning (ML) can be applied, and captures information along…
Recently, adaptive control systems with relaxed persistent excitation (PE) conditions have been proposed to guarantee true parameter convergence and improve the transient response. However, in some cases, sufficient control performance and…
Laminar drag reduction is a critical technology for enhancing the endurance and station-keeping capabilities of airship platforms. However, existing transport-based transition models fail to account for the premature transition induced by…
This paper extends the high-order entropy stable (ES) adaptive moving mesh finite difference schemes developed in [14] to the two- and three-dimensional (multi-component) compressible Euler equations with the stiffened equation of state.…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
For autoregressive modeling of chaotic dynamical systems over long time horizons, the stability of both training and inference is a major challenge in building scientific foundation models. We present a hybrid technique in which an…
This paper provides an exponential stability result for the adaptive anti-unwinding attitude tracking control problem of a rigid body with uncertain but constant inertia parameters, without requiring the satisfaction of persistent…
Fast and accurate optimization and simulation is widely becoming a necessity for large scale transmission resiliency and planning studies such as N-1 SCOPF, batch contingency solvers, and stochastic power flow. Current commercial tools,…
Conformal prediction (CP) provides a comprehensive framework to produce statistically rigorous uncertainty sets for black-box machine learning models. To further improve the efficiency of CP, conformal correction is proposed to fine-tune or…
It is well known that viable architectural structures can be identified by locating the critical points of the gravitational potential energy congruent with some fixed surface metric. This is because, if the walls are thin, the lowest…
Computing the receding horizon optimal control of nonlinear hybrid systems is typically prohibitively slow, limiting real-time implementation. To address this challenge, we propose a layered Model Predictive Control (MPC) architecture for…
Trajectory prediction (TP) is crucial for ensuring safety and efficiency in modern air traffic management systems. It is, for example, a core component of conflict detection and resolution tools, arrival sequencing algorithms, capacity…
Simulated annealing solves global optimization problems by means of a random walk in a cooling energy landscape based on the objective function and a temperature parameter. However, if the temperature is decreased too quickly, this…
Paleoclimate proxy records and models suggest that the Atlantic Meridional Overturning Circulation (AMOC) can transition abruptly between a strong and a weak state. Empirical warning signals in observational fingerprints indeed suggest a…
We study adaptive network models in which coupling weights evolve on a fast time scale relative to the phase dynamics of the nodes. Using Geometric Singular Perturbation Theory (GSPT), we prove that, although the microscopic system is…
Rank collapse, a phenomenon where embedding vectors in sequence models rapidly converge to a uniform token or equilibrium state, has recently gained attention in the deep learning literature. This phenomenon leads to reduced expressivity…
Pillars are important structural units used to ensure mining safety in underground hard rock mines. Therefore, precise predictions regarding the stability of underground pillars are required. One common index that is often used to assess…
Continual learning is an essential capability of human cognition, yet it poses significant challenges for current deep learning models. The primary issue is that new knowledge can interfere with previously learned information, causing the…
This paper presents the development and analysis of an asymptotically compatible (AC) unfitted finite element method for one-dimensional nonlocal elliptic interface problems. The proposed method achieves optimal error estimates through…
Standard conformal anomaly detection provides marginal finite-sample guarantees under the assumption of exchangeability . However, real-world data often exhibit distribution shifts, necessitating a weighted conformal approach to adapt to…